The heat of combustion of ethanol into carbon dioxide and water is – 327 kcal at constant pressure. The heat evolved (in

The ratio of the mass percentages of ‘C & H’ and ‘C & O’ of a saturated acyclic organic compound ‘X’ are 4 : 1 a

For the disproportionation reaction 2Cu+(aq) ⇌ Cu(s) + Cu2+(aq) at 298 K. ln K (where K is the equilibrium constant) is

The oxidation states of transition metal atoms in K2Cr2O7, KMnO4 and K2FeO4, respectively, are x, y and z. The sum of x,

The work function of sodium metal is 4.41 $$ \times $$ 10–19 J. If photons of wavelength 300 nm are incident on the meta

The correct observation in the following reactions is :

The major product of the following reaction is :

The shape / structure of [XeF5]– and XeO3F2, respectively, are

An organic compound ‘A’ (C9H10O) when treated with conc. HI undergoes cleavage to yield compounds ‘B’ and ‘C’. ‘B’ gives

Two compounds A and B with same molecular formula (C3H6O) undergo Grignard’s reaction with methylmagnesium bromide to gi

The molecular geometry of SF6 is octahedral. What is the geometry of SF4 (including lone pair(s) of electrons, if any)?

The results given in the below table were obtained during kinetic studies of the following reaction 2A + B $$ \to $$ C +

Match the type of interaction in column A with the distance dependence of their interaction energy in column B .tg {bo

The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution. Which one of the follo

The one that is not expected to show isomerism is :

Simplified absorption spectra of three complexes ((i), (ii) and (iii)) of Mn+ ion are provided below; their $$\lambda $$

If you spill a chemical toilet cleaning liquid on your hand, your first aid would be

The number of subshells associated with n = 4 and m = –2 quantum numbers is

Consider the reaction sequence given below: Which of the following statements is true?

Arrange the following labelled hydrogens in decreasing order of acidity :

The major product obtained from E2 - elimination of 3-bromo-2-fluoropentane is

Three elements X, Y and Z are in the 3rd period of the periodic table. The oxides of X, Y and Z, respectively, are basic

Let a, b, c $$ \in $$ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = $$\left( {\matrix{ a & b

If the equation cos4 $$\theta $$ + sin4 $$\theta $$ + $$\lambda $$ = 0 has real solutions for $$\theta $$, then $$\lambd

Let f : R $$ \to $$ R be a function which satisfies f(x + y) = f(x) + f(y) $$\forall $$ x, y $$ \in $$ R. If f(1) = 2 an

Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair o

The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the ve

Let f : (–1, $$\infty $$) $$ \to $$ R be defined by f(0) = 1 and f(x) = $${1 \over x}{\log _e}\left( {1 + x} \right)$$,

Let A = {X = (x, y, z)T: PX = 0 and x2 + y2 + z2 = 1} where $$P = \left[ {\matrix{ 1 & 2 & 1 \cr { - 2}

Let the position vectors of points 'A' and 'B' be $$\widehat i + \widehat j + \widehat k$$ and $$2\widehat i + \widehat

Let [t] denote the greatest integer less than or equal to t. Then the value of $$\int\limits_1^2 {\left| {2x - \left[ {3

If y = $$\sum\limits_{k = 1}^6 {k{{\cos }^{ - 1}}\left\{ {{3 \over 5}\cos kx - {4 \over 5}\sin kx} \right\}} $$, then $$

If the variance of the terms in an increasing A.P., b1 , b2 , b3 ,....,b11 is 90, then the common difference of this A.P

The set of all possible values of $$\theta $$ in the interval (0, $$\pi $$) for which the points (1, 2) and (sin $$\the

If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x2dy= (2xy + y2)dx

Consider a region R = {(x, y) $$ \in $$ R : x2 $$ \le $$ y $$ \le $$ 2x}. if a line y = $$\alpha $$ divides the area of

Let EC denote the complement of an event E. Let E1 , E2 and E3 be any pairwise independent events with P(E1) > 0 a

For some $$\theta \in \left( {0,{\pi \over 2}} \right)$$, if the eccentricity of the hyperbola, x2–y2sec2$$\theta $$ =

$$\mathop {\lim }\limits_{x \to 0} {\left( {\tan \left( {{\pi \over 4} + x} \right)} \right)^{{1 \over x}}}$$ is equal

The imaginary part of $${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1

If the sum of first 11 terms of an A.P., a1, a2, a3, .... is 0 (a $$ \ne $$ 0), then the sum of the A.P., a1 , a3 , a5 ,

An inductance coil has a reactance of 100 $$\Omega $$. When an AC signal of frequency 1000 Hz is applied to the coil, th

In the following digital circuit, what will be the output at ‘Z’, when the input (A, B) are (1, 0), (0, 0), (1, 1,), (0,

A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface

Two uniform circular discs are rotating independently in the same direction around their common axis passing through the

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electri

The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the eart

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of t

A 10 $$\mu $$F capacitor is fully charged to a potential difference of 50 V. After removing the source voltage it is con

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to ea

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface

The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region wi

The displacement time graph of a particle executing S.H.M is given in figure :(sketch is schematic and not to scale) Wh

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energ

In a hydrogen atom the electron makes a transition from (n + 1)th level to the nth level. If n >> 1, the frequency

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are

In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of a waveleng

When the temperature of a metal wire is increased from 0oC to 10oC, its length increases by 0.02%. The percentage change

An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is 2 $$\Omega $$. The potential diffe

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $$\widehat k$$ a

A square shaped hole of side l = $${a \over 2}$$ is carved out at a distance d = $${a \over 2}$$ from the centre ‘O’ of

A particle of mass m is moving along the x-axis with initial velocity $$u\widehat i$$. It collides elastically with a pa

A light ray enters a solid glass sphere of refractive index $$\mu $$ = $$\sqrt 3 $$ at an angle of incidence 60o. The ra

A wire of density 9 $$ \times $$ 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wir